Biprateep Dey

Thomas Y. Chen, Biprateep Dey, Aishik Ghosh et al.

Estimating uncertainty is at the core of performing scientific measurements in HEP: a measurement is not useful without an estimate of its uncertainty. The goal of uncertainty quantification (UQ) is inextricably linked to the question, "how do we physically and statistically interpret these uncertainties?" The answer to this question depends not only on the computational task we aim to undertake, but also on the methods we use for that task. For artificial intelligence (AI) applications in HEP, there are several areas where interpretable methods for UQ are essential, including inference, simulation, and control/decision-making. There exist some methods for each of these areas, but they have not yet been demonstrated to be as trustworthy as more traditional approaches currently employed in physics (e.g., non-AI frequentist and Bayesian methods). Shedding light on the questions above requires additional understanding of the interplay of AI systems and uncertainty quantification. We briefly discuss the existing methods in each area and relate them to tasks across HEP. We then discuss recommendations for avenues to pursue to develop the necessary techniques for reliable widespread usage of AI with UQ over the next decade.

Biprateep Dey, David Zhao, Brett H. Andrews et al.

Key science questions, such as galaxy distance estimation and weather forecasting, often require knowing the full predictive distribution of a target variable $y$ given complex inputs $\mathbf{x}$. Despite recent advances in machine learning and physics-based models, it remains challenging to assess whether an initial model is calibrated for all $\mathbf{x}$, and when needed, to reshape the densities of $y$ toward "instance-wise" calibration. This paper introduces the LADaR (Local Amortized Diagnostics and Reshaping of Conditional Densities) framework and proposes a new computationally efficient algorithm ($\texttt{Cal-PIT}$) that produces interpretable local diagnostics and provides a mechanism for adjusting conditional density estimates (CDEs). $\texttt{Cal-PIT}$ learns a single interpretable local probability--probability map from calibration data that identifies where and how the initial model is miscalibrated across feature space, which can be used to morph CDEs such that they are well-calibrated. We illustrate the LADaR framework on synthetic examples, including probabilistic forecasting from image sequences, akin to predicting storm wind speed from satellite imagery. Our main science application involves estimating the probability density functions of galaxy distances given photometric data, where $\texttt{Cal-PIT}$ achieves better instance-wise calibration than all 11 other literature methods in a benchmark data challenge, demonstrating its utility for next-generation cosmological analyses.

Biprateep Dey, Jeffrey A. Newman, Brett H. Andrews et al.

Many astrophysical analyses depend on estimates of redshifts (a proxy for distance) determined from photometric (i.e., imaging) data alone. Inaccurate estimates of photometric redshift uncertainties can result in large systematic errors. However, probability distribution outputs from many photometric redshift methods do not follow the frequentist definition of a Probability Density Function (PDF) for redshift -- i.e., the fraction of times the true redshift falls between two limits $z_{1}$ and $z_{2}$ should be equal to the integral of the PDF between these limits. Previous works have used the global distribution of Probability Integral Transform (PIT) values to re-calibrate PDFs, but offsetting inaccuracies in different regions of feature space can conspire to limit the efficacy of the method. We leverage a recently developed regression technique that characterizes the local PIT distribution at any location in feature space to perform a local re-calibration of photometric redshift PDFs. Though we focus on an example from astrophysics, our method can produce PDFs which are calibrated at all locations in feature space for any use case.